The electrode potential of a chlorine electrode is maximum when the concentration of chloride ion in the solution (in $mol \ L^{-1}$) is $X$. What is the value of $X$?

For $Cr_2O_7^{2-} + 14H^{+} + 6e^- \longrightarrow 2Cr^{3+} + 7H_2O$,$E^0 = 1.33 \ V$. Given $[Cr_2O_7^{2-}] = 4.5 \ mmol$,$[Cr^{3+}] = 1.5 \ mmol$ and $E = 1.067 \ V$,calculate the $pH$ of the solution.

At $25\,^{\circ}C$,calculate the equilibrium constant for the cell reaction,
$X_{(s)} + Y_{(aq)}^{2+} \rightleftharpoons Y_{(s)} + X_{(aq)}^{2+}$
Given:
$E_{X^{2+}/X}^{o} = -1.36\,V$;
$E_{Y^{2+}/Y}^{o} = -0.76\,V$; $\frac{2.303\,RT}{F} = 0.06$

Calculate the equilibrium constant $(K_C)$ for the cell obtained by connecting two electrodes with standard electrode potentials $E^o_{(Sn^{2+}|Sn)} = -0.14 \ V$ and $E^o_{(Ni^{2+}|Ni)} = -0.23 \ V$ at $298 \ K$.

$E_{cell}^{0}$ of the reaction $Mg_{(s)} + 2 Ag_{(0.0001 \ M)}^{+} \rightleftharpoons Mg_{(0.01 \ M)}^{2+} + 2 Ag_{(s)}$ is $3.17 \ V$. The $E_{cell}$ of the reaction and its cell notation respectively are :

To find the standard potential of $M^{3+}/M$ electrode,the following cell is constituted:
$Pt | M | M^{3+} (0.001 \ mol \ L^{-1}) || Ag^{+} (0.01 \ mol \ L^{-1}) | Ag$
The $emf$ of the cell is found to be $0.421 \ V$ at $298 \ K$. The standard potential of the half-reaction $M^{3+} + 3e^{-} \to M$ at $298 \ K$ will be .............. $V$.
(Given $E^{o}_{Ag^{+}/Ag}$ at $298 \ K = 0.80 \ V$)